Release List Reviews Shop Join News DVD Giveaways Video Games Advertise
DVD Reviews | Theatrical Reviews | Adult DVD Reviews | Video Game Reviews | Price Search Buy Stuff Here
DVD Talk
DVD Reviews DVD Talk Headlines HD Reviews


Add to My Yahoo! - RSS 2.0 - RSS 2.0 - DVD Talk Podcast RSS -


Go Back   DVD Talk Forum > General Discussions > Other Talk

Other Talk "Otterville" plus Religion/Politics

Reply
 
Thread Tools
Old 06-01-06, 04:22 PM   #1
Heat
DVD Talk Legend
 
Join Date: Dec 2000
Location: Central Illinois
Posts: 16,542
Probability

1. Suppose you're on a game show and you're given the choice of three doors. Behind one is a car, behind each of the others is a goat. You pick a door, say door A, and the host, who knows what's behind the other doors, opens another door, say B, which has a goat. He then says : "Do you want to switch to door C?" Is it to your advantage to take the switch?'

2. There is a card in a hat. It is either the ace of spades or the king of spades, with equal probability. You take another identical ace of spades and throw it into the hat. You then choose a card at random from the hat. You see it is an ace. What are the odds the original card in the hat was an ace?

3. You meet a woman who has a son in your child's class. She says "I have two children". So, at this point, you know that the woman has two children and at least one of those two children is a boy. What is the probability that this woman has two boys?

4. The same woman's two children come to visit you. The boy from your child's class enters your house and the woman's second child knocks on the door. What is the probability that the woman has two boys?

5. There's a lottery with 10,000 "scratch-off-the-dot" tickets with one ticket being the winner of a car, the other 9,999 tickets being losers.

Ten thousand people buy the tickets, including you. 9,998 scratch off the dots on their tickets and find the message YOU LOSE. Should you offer big money to the remaining ticketholder to exchange tickets with you?

Spoilerize any answers...

Question 1:
Spoiler:
Yes, switch. There is a 2/3 chance that Door C will be the winner.


Question 2:
Spoiler:
The answer is 2/3.


Question 3:
Spoiler:
The answer is 1/3.


Question 4:
Spoiler:
The answer is 1/2.


Question 5:
Spoiler:
5. No (you both have the same probability of winning).

Last edited by Heat; 06-01-06 at 04:24 PM.
  Reply With Quote
Old 06-01-06, 04:23 PM   #2
Minor Threat
DVD Talk Legend
 
Minor Threat's Avatar
 
Join Date: Jul 2000
Posts: 13,665
I'd whip out my STOAP infused gum and vigorously chew until I had the answer.....
__________________
"I think they go by username, so you're probably not a very high priority at the moment." - dork
  Reply With Quote
Old 06-01-06, 04:26 PM   #3
Charlie Goose
DVD Talk Legend
 
Charlie Goose's Avatar
 
Join Date: Jul 2000
Location: Sesame Street (the apt. next to Bob's)
Posts: 20,201
1. There are 100 threads created each day in Other. What is the probability that this one will suck?

Question 1:
Spoiler:
100%












__________________
Ohwa Tagu Siam
  Reply With Quote
Old 06-01-06, 04:28 PM   #4
GatorDeb
DVD Talk Legend
 
GatorDeb's Avatar
 
Join Date: Mar 2001
Location: The "Real" Vice City
Posts: 15,193
Spoiler:
Why are three and four not the same?
__________________
XBOX Live Gamertag: GatorDeb07 (zero seven)
My XBOX 360 blogs about me
"Polo por u, polo por u" - Peggy speaking Spanish from KOTH (Chicken for you, chicken for you)
  Reply With Quote
Old 06-01-06, 04:38 PM   #5
4KRG
DVD Talk Legend
 
Join Date: Jan 2000
Posts: 15,727
Please show your math, otherwise it looks like you cheated
  Reply With Quote
Old 06-01-06, 04:44 PM   #6
Bushdog
DVD Talk Hero
 
Join Date: Dec 1999
Location: Shackled
Posts: 35,372
Quote:
Originally Posted by GatorDeb
Spoiler:
Why are three and four not the same?
Spoiler:
Yeah, this one kind of depends on the perspective.

The possible combinations of two kids are:
1) MM
2) MF
3) FM
4) FF

In three, we can exclude possibility #4 (FF) thus 1/3rd.

In 4, we are taking only the gender of this child into account, we are essentially assuming the gender of the first child as male. By doing this, we eliminate choice 4 still (FF) as well as choice 3 (FM, the first child being a female since the first child is a male based on observation)).

In three, the first child could be of either gender, thus options 2 and 3 are both valid. Not so in the 2nd scenario.
  Reply With Quote
Old 06-01-06, 04:49 PM   #7
Heat
DVD Talk Legend
 
Join Date: Dec 2000
Location: Central Illinois
Posts: 16,542
Show my math on which one?

Questions 1 and 3
Spoiler:
are classic Marilyn Von Savant questions (from the early to mid 1990s), both of these stumped quite a few people including math professors but the answers I showed are correct.

The key to question 1 is that the game show host knows which door is not a winner. The key to question 3 is that you donít know whether the boy is the older or younger child thus the possibilities are still boy-girl / girl-boy / boy-boy. Thereís a one-third chance that itís boy-boy. (see Bushdog's explanation).


Question 2
Spoiler:
is simple odds. There are only three possibilities:
a. You put an ace in the hat and pull this ace out.
b. You put an ace in the hat and pull the 2nd ace out.
c. You put a king in the hat and pull the 2nd ace out.
Thereís a 2/3 chance that the original card was an ace.


Question 4:
Spoiler:
In question 3 you didnít know whether the child was the older or younger child. In question 4 youíre looking at only one child, the second child, so itís back to a 50/50 chance.


Question 5:
Spoiler:
I donít think that anybody had any trouble with Question 5.
  Reply With Quote
Old 06-01-06, 04:56 PM   #8
BravesMG
DVD Talk Hall of Fame
 
Join Date: Dec 2000
Posts: 7,937
It's been a while since my last probabilities class, but #1 confuses me.

Spoiler:
Isn't there a principle that if all elements of an equation are unknown, their properties are equal no matter what else in the equation changes? I remember a question like this on an exam, and I'm pretty sure I got it wrong then too, but if it was true that your odds do increase by switching from your initial selection to which ever door you did not choose, wouldn't it be the same if you reversed your initial selections? So it couldn't possibly increase your odds in both cases? I know I'm probably wrong on this, but I could use some help.


I just read the above post regarding #1, but I'm still confused as to how
Spoiler:
because the host knows what is behind each door, why that matters to the probability of the contestant.

Last edited by bravesmg; 06-01-06 at 05:00 PM.
  Reply With Quote
Old 06-01-06, 04:58 PM   #9
Bushdog
DVD Talk Hero
 
Join Date: Dec 1999
Location: Shackled
Posts: 35,372
This is a long discussion and I'm too lazy to get into it.

Google "Monty Hall Problem" and all your questions will be answered.
  Reply With Quote
Old 06-01-06, 05:01 PM   #10
das Monkey
DVD Talk Hero
 
das Monkey's Avatar
 
Join Date: May 1999
Location: Atlanta, GA
Posts: 35,881
#1 is one of my favorites. Whenever someone is posturing about how smart he thinks he is, I'll break it out. A guy at work wrote a computer program to "prove me wrong". That didn't work out the way he wanted.

bravesmg, the question is worded somewhat poorly above. The key to the problem is that the host always shows you a bad prize (goat) before asking you to switch.

das
__________________
Dragon*Con 2004 - 2005 - Lost in Hawaii - DVD Reviews

You are not entitled to your own opinion. You are only entitled to your own informed opinion. -- Harlan Ellison quoting Gustave Flaubert

Last edited by das Monkey; 06-01-06 at 05:04 PM.
  Reply With Quote
Old 06-01-06, 05:05 PM   #11
Mopower
DVD Talk Legend
 
Mopower's Avatar
 
Join Date: Nov 2001
Location: The Janitor's closet in Kinnick Stadium
Posts: 15,725
Spoiler:
I just wanted to spoilerize something like everyone else has.
  Reply With Quote
Old 06-01-06, 05:10 PM   #12
das Monkey
DVD Talk Hero
 
das Monkey's Avatar
 
Join Date: May 1999
Location: Atlanta, GA
Posts: 35,881
If you want an explanation for #1 that's simple to understand:

Spoiler:
You have 3 doors. You pick 1. The probability you chose the car is 1/3. The probability you didn't is 2/3. Whether he shows you what's behind one of the doors or all the doors for that matter, those numbers don't change. There's a 2/3 chance you picked the wrong door. By eliminating one of the doors you didn't pick and allowing you to switch to the other, he's essentially allowing you to pick both of those doors at the same time.


das
__________________
Dragon*Con 2004 - 2005 - Lost in Hawaii - DVD Reviews

You are not entitled to your own opinion. You are only entitled to your own informed opinion. -- Harlan Ellison quoting Gustave Flaubert
  Reply With Quote
Old 06-01-06, 05:12 PM   #13
kvrdave
DVD Talk God
 
kvrdave's Avatar
 
Join Date: Aug 1999
Location: Pacific NW
Posts: 81,709
Quote:
Originally Posted by bravesmg
I just read the above post regarding #1, but I'm still confused as to how
Spoiler:
because the host knows what is behind each door, why that matters to the probability of the contestant.
Here is the dumbed down version that I use because I am dumbed down....
Spoiler:
When you initially start, you have a 33% chance of getting the correct door. Once a door is taken away, you can either sit on your original 33% chance of being right or move to a 50% chance of being right. Yeah, I know, it seems like word trickery, but it ain't....it's powerful magic.
__________________
Of all tyrannies a tyranny sincerely exercised for the good of its victim may be the most oppressive. It may be better to live under robber barons than under omnipotent moral busybodies. The robber baronís cruelty may sometimes sleep, his cupidity may at some point be satiated, but those who torment us for our own good will torment us without end for they do so with the approval of their own conscience. - C.S. Lewis
  Reply With Quote
Old 06-01-06, 05:15 PM   #14
BravesMG
DVD Talk Hall of Fame
 
Join Date: Dec 2000
Posts: 7,937
I know it was poorly worded, I'm usually right on probability, I've got an Economics degree, but this always has baffled me. I'm going into the web explanations now.
  Reply With Quote
Old 06-01-06, 05:19 PM   #15
Kittydreamer
DVD Talk Legend
 
Kittydreamer's Avatar
 
Join Date: Jun 2004
Location: Portland, OR
Posts: 13,609
Quote:
Originally Posted by Mopower
Spoiler:
I just wanted to spoilerize something like everyone else has.
Spoiler:
I don't know how to do spoiler tags and had to quote you so I could figure it out. I also don't know how to do probablity stuff. I'm useless.
__________________
Quote:
DeputyDave: You can take my ocelot when you can pry it off of my cold dead penis.
  Reply With Quote
Old 06-01-06, 05:23 PM   #16
deadlax
DVD Talk Gold Edition
 
Join Date: Nov 2000
Location: Decatur, GA
Posts: 2,148
Spoiler:
#1 is hands down the dumbest "brain teaser" of all-time. Granted you get to "choose" both doors, after door B is open you have a 50/50 shot at guessing the correct door. It is either a or c. Once that information has been given to all participants in the game the odds have been shifted.

You can try to stump brilliant people all the time with this. And I get why it makes "statistical" sense to make the switch. But it doesn't make common sense to make the switch.

Last edited by deadlax; 06-01-06 at 05:27 PM.
  Reply With Quote
Old 06-01-06, 05:27 PM   #17
das Monkey
DVD Talk Hero
 
das Monkey's Avatar
 
Join Date: May 1999
Location: Atlanta, GA
Posts: 35,881
Quote:
ē deadlax ē

Spoiler:
#1 is hands down the dumbest "brain teaser" of all-time. Granted you get to "choose" both doors, after door B is open you have a 50/50 shot at guessing the correct door. It is either a or c. Once that information has been given to all participants in the game the odds have been shifted.

You can try to stump brilliant people all the time with this. And I get why it makes "statistical" sense to make the switch. But it doesn't make common sense to make the switch.


Too many people think with their brains instead of feeling with their gut.

das
__________________
Dragon*Con 2004 - 2005 - Lost in Hawaii - DVD Reviews

You are not entitled to your own opinion. You are only entitled to your own informed opinion. -- Harlan Ellison quoting Gustave Flaubert
  Reply With Quote
Old 06-01-06, 05:30 PM   #18
Bushdog
DVD Talk Hero
 
Join Date: Dec 1999
Location: Shackled
Posts: 35,372
Spoiler:
Probabilistic sense, not statistical sense. They are different things.
  Reply With Quote
Old 06-01-06, 05:31 PM   #19
OldDude
DVD Talk Legend
 
Join Date: Jul 2001
Location: MI
Posts: 24,759
Spoiler:
I don't buy the answer on number 1. The logic (not the numvers) of #1 and #5 are identical. The original odds are changed once you rule out a bunch of losers, but the new odds are equal amongst the remaining choices as no winners have been revealed. Both the remaining doors have 50% odds.
Actually, my analysis assumes the host ALWAYS shows you a goat, and offers to let you switch. If he does so selectively, then the game is rigged. The odds of whether it is rigged for you or against can not be estimated from the problem statement.

Further, the two kids problems, #3 and #4 have the same logic and same answer 50%. Nothing about the boy you know about changes the odds of the other kid. Actually the odds of a boy are slightly higher than 50% based on birth rates. I'm too lazy to go dig for the exact number.
__________________
9/11/2001 - You have awakened a sleeping giant, and filled him with a terrible resolve. - paraphrased from Yamamoto
  Reply With Quote
Old 06-01-06, 05:34 PM   #20
Heat
DVD Talk Legend
 
Join Date: Dec 2000
Location: Central Illinois
Posts: 16,542
All-right, Iíll make the call. Once page 2 starts, spoiler tags arenít needed anymore.

Originally posted by Old Dude
Quote:
Spoiler:
Further, the two kids problems, #3 and #4 have the same logic and same answer 50%. Nothing about the boy you know about changes the odds of the other kid. Actually the odds of a boy are slightly higher than 50% based on birth rates. I'm too lazy to go dig for the exact number.
It's something like 109 boys for every 100 girls, but girls have a higher childhood survival rate.
Spoiler:
And it's tricky, but the key is that you don't know whether the boy in the classroom is the older or younger sibling. When the kid knocks on the door, order doesn't matter since you are only looking at one child at that point.

Last edited by Heat; 06-01-06 at 05:39 PM.
  Reply With Quote
Old 06-01-06, 05:47 PM   #21
talemyn
DVD Talk Limited Edition
 
Join Date: Sep 2003
Location: Charlotte, NC
Posts: 7,466
Quote:
Originally Posted by OldDude
Spoiler:
I don't buy the answer on number 1. The logic (not the numvers) of #1 and #5 are identical. The original odds are changed once you rule out a bunch of losers, but the new odds are equal amongst the remaining choices as no winners have been revealed. Both the remaining doors have 50% odds.
Actually, my analysis assumes the host ALWAYS shows you a goat, and offers to let you switch. If he does so selectively, then the game is rigged. The odds of whether it is rigged for you or against can not be estimated from the problem statement.

Further, the two kids problems, #3 and #4 have the same logic and same answer 50%. Nothing about the boy you know about changes the odds of the other kid. Actually the odds of a boy are slightly higher than 50% based on birth rates. I'm too lazy to go dig for the exact number.
I agree with you on the first question. I always hated that one (and argued with my professor about it for a long time). I still don't agree with the "official" answer.

Of course I was hesitant to post that I agreed with you because you are completely wrong about questions 3 and 4.
__________________
Hooray for sarcasm:
"I laughed so hard, I vomited a little." - Cornelius1047
"G** d*** you guys and your photoshops. You're all sick, demented individuals. I have no clue how I'm going to explain those to him." - WhoGirl

WAR EAGLE! <--- "If you look up 'good person' in the dictionary, this is the person you will find." - twikoff
  Reply With Quote
Old 06-01-06, 05:51 PM   #22
OldDude
DVD Talk Legend
 
Join Date: Jul 2001
Location: MI
Posts: 24,759
Quote:
Originally Posted by Heat
[b]
Spoiler:
And it's tricky, but the key is that you don't know whether the boy in the classroom is the older or younger sibling. When the kid knocks on the door, order doesn't matter since you are only looking at one child at that point.
Spoiler:
I don't see that the order matters. You know one child is a boy your child's age (close enough for same class) and you don't know shit about the other child, so the odds are (roughly 50/50.


Are these questions from this month's "Lies, Damned lies, Statistics."

Edit: Ok, I'm wrong on #1, and the Wikipedia entry offers analysis from several points of view. At least one will be compelling.
__________________
9/11/2001 - You have awakened a sleeping giant, and filled him with a terrible resolve. - paraphrased from Yamamoto

Last edited by OldDude; 06-01-06 at 06:13 PM.
  Reply With Quote
Old 06-01-06, 06:45 PM   #23
shaun3000
DVD Talk Hall of Fame
 
Join Date: Jul 1999
Location: Dallas, Texas
Posts: 7,754
I agree that #1 is stupid.
  Reply With Quote
Old 06-01-06, 07:12 PM   #24
El Scorcho
DVD Talk Hero
 
El Scorcho's Avatar
 
Join Date: Jun 2000
Location: Portland, OR
Posts: 39,619
As always, wikipedia explains things better than you shlubs.
  Reply With Quote
Old 06-01-06, 07:48 PM   #25
dork
DVD Talk Legend
 
Join Date: Jul 2001
Posts: 10,547
Quote:
Originally Posted by OldDude
Spoiler:
I don't see that the order matters. You know one child is a boy your child's age (close enough for same class) and you don't know shit about the other child, so the odds are (roughly 50/50.
#3 is poorly phrased, but the point is that
Spoiler:
you supposedly don't know which of her two sons is in your child's class (if she, in fact, has two sons). So that adds another possible event. However, in #4 you already see one son so the probability that the other child is a boy is now 1/2. It's like you collapsed the wave function.
  Reply With Quote
Sponsored Links
Reply

Thread Tools

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is On
Trackbacks are Off
Pingbacks are Off
Refbacks are Off


All times are GMT -5. The time now is 03:18 PM.

Rules - DVD Talk - Archive - Privacy Statement - Top

Powered by vBulletin® Version 3.7.2
Copyright ©2000 - 2014, Jelsoft Enterprises Ltd.
Content Relevant URLs by vBSEO 3.2.0
Copyright 2011 DVDTalk.com All Rights Reserved. Privacy Policy and Terms of Use.